Nanoparticles are currently the subject of intense study as surveyed, for example, in G. Schmid, ed., Nanoparticles: From Theory to Application (Wiley, 2004), which is incorporated herein by reference. Applications are as diverse as drug delivery, sensing, bio-imaging and sorbent manufacture. Not least among the interesting properties of nanoparticles are their optical characteristics. The optical attributes of nanoparticles are observed in familiar materials such as opal and stained glass. More recently the optical properties of nanostructures have been exploited in applications such as the construction of metamaterials, discussed by Ziolkowski et al., eds., Metamaterials: Physics and Engineering Explorations (Wiley, 2006), and the subwavelength containment of fields using optical antennas, as discussed by Mühlschlegel et al., Resonant optical antennas, Science, 308, 1607-1609 (2005). With the increasing use of nanoparticles in optical applications it is desirable to be able to characterize the optical response of a single nanoparticle. This work focuses on the elastic scattering properties, which are determined by a wavelength-dependent linear polarizability tensor for sufficiently small nanoparticles.
The polarizability of a nanoparticle is determined both by the constituent material and by the particle size and shape. For purposes of the present description, unless the particular context requires otherwise, the term “nanoparticle” will refer to a scatterer having point-like characteristics, in that its overall dimensions are smaller than the diffraction limit of any radiation used in its characterization. For a known material and geometry, the polarizability may be determined analytically or by computational methods, however, small deviations from the specified shape may introduce significant optical changes—see Canfield et al., Chirality arising from small defects in gold nanoparticle arrays, Optics Express 14, 950-955 (2006) for related measurements from nanoparticle arrays. It is, therefore, highly desirable that a means be provided for actually measuring the polarizability using far-field optical measurements, and that is provided by the current invention, as discussed below.
The measurement scheme of the present invention is based on a coherent confocal microscope. Coherent microscopes use interference with a reference beam to holographically record data and hence acquire information regarding the phase of the measured field. While coherent microscopy predates the invention of the laser, modern bright and broadband sources have made spectrally-sensitive coherent microscopy a practical methodology. This is evidenced by the popularity of techniques such as optical coherence tomography (OCT).
In addition to collecting phase-sensitive data, a coherent microscope has the advantage of high sensitivity when compared to a traditional intensity-based system. As a result, coherent microscopy is suitable for true nanoimaging, as demonstrated by results such as the interferometric detection of single viruses and gold particles as small as 5 nm, as reported by Ignatovich et al., Real-time and background-free detection of nanoscale particles, Phys. Rev. Lett., 96, article no. 013,901 (2006).
In coherent microscopy the optical source is usually split into a reference field and a field that is used to illuminate the sample. The light returned from the sample is combined with the reference field and the interferometric features in the data are used for image formation. To exhibit interference the returned light must be coherent with the reference field and at the same wavelength. This means that potentially useful signals from a nanoparticle, such as Raman-scattered, higher-harmonic and/or fluorescent light, are not detected. As a result, the coherent microscope described here is used to measure only the linear component of the nanoparticle polarizability and the three-dimensional position of the nanoparticle.
Traditional microscopy and spectroscopy usually involve the formation of a scalar image on spatial and/or spectral axes. While this image is immediately useful in many applications, it is possible to design sensing systems that form non-scalar images and/or exploit less obvious relationships between the collected data and the imaged objects. A comprehensive discussion is provided by Barrett et al., Foundations of Image Science (Wiley-Interscience, 2003), which is incorporated herein by reference. For example, many modern microscopy and imaging systems collect images as a function of polarization state and/or scattering angle. Additionally, in some applications the object can be represented by a small number of parameters which are estimated from the data with very high precision. In single molecule microscopy, the a priori knowledge that the object can be parameterized by the molecule location allows the molecule to be localized with a precision orders of magnitude better than the diffraction limit.